Question

I need help, please?

Answer 1

x is timed by .5 in the first one (A) which would make it the linear function.

Answer 2

For this case we observe that the first table has a constant rate of change.

In linear functions, the rate of change is constant.

To prove it, we will find the rate of change for two different intervals.

Interval 1:

$m = \frac{1-\frac{1}{2}}{2-1}$

$m = \frac{\frac{1}{2}}{1}$

$m = \frac{1}{2}$

Interval 2:

$m = \frac{2-\frac{1}{2}}{4-1}$

$m = \frac{\frac{3}{2}}{3}$

$m = \frac{3}{6}$

$m = \frac{1}{2}$

Since the rate of change is constant, then the function is linear.

Answer:

The first table is a linear function.